Bromsgrove District Council lists 12 conservation areas: Alvechurch, Barnt Green, Belbroughton, Beoley, Bromsgrove Town Centre, Clent, Dodford, Hagley, Hewell Grange, Holy Cross, St John's and the Worcester and Birmingham Canal. Two cover the town itself, Bromsgrove Town Centre and St John's.
The Bromsgrove Town conservation area was designated by Worcestershire County Council in 1968 and extended in 1983 and 1989. Its character appraisal records buildings from the sixteenth century onwards, timber framed with wattle and daub and brick infill panels, notes that some brick buildings have been painted, and records white stucco and render in a few cases. The council publishes no separate lime or breathable finish guidance.
We would explain how you check the conservation boundary, any Article 4 direction and the proposed work before confirming whether permission is needed. That answers it on the render page instead of on site.